FP in Scala 4 - 4.3, 4.4, 4.4

gistfile1.scala

/**
 * Created by BPK_t on 2015/06/19.
 */
object Main {
  def main(args: Array[String]) {

    val a = Some(100)
    val b = Some(200.0)

    val c = map2(a,b)((x,y)=>x+y)
    println(c)

    val x = sequence(List(Some(1),Some(2),Some(3)))
    println(x)

    val x2 = sequence(List(Some(1),None,Some(3)))
    println(x2)

    val y = traverse(List("1", "2", "3"))(x => Some(x.toInt))
    println(y)
  }

  //4.3
  def map2[A,B,C](a:Option[A], b:Option[B])(f:(A,B)=>C) : Option[C] = {
    a.flatMap(x => b.map(y => f(x,y)))
  }

  //4.4
  def sequence[A](a:List[Option[A]]):Option[List[A]] = a match {
    case Nil => Some(Nil)
    case _ => map2(a.head, sequence(a.tail))(_ :: _)
  }

  //4.5
  def traverse[A, B](a: List[A])(f: A => Option[B]): Option[List[B]] = {
    a match {
      case Nil => Some(Nil)
      case _ => map2(f(a.head), traverse(a.tail)(f))(_ :: _)
    }
  }
}